Question

A school has a hall which is 22 m long and 15.5 m broad. A carpet is laid inside the hall
leaving all around a margin of 75 cm from the walls. Find the area of the carpet and the
area of the strip left uncovered. If the width of the carpet is 82 cm. ſind its cost at the rate of
60 per m.
​

Answer 1

Answer:

Area of the carpet = 287m²

Area of the strip left uncovered = 54m²

Cost of fencing = Rs. 21000

Step-by-step explanation:

length = 22m

breadth = 15.5m

the area of the hall = L × B = 22 × 15.5 = 341m²

margin of carpet = 75cm = 0.75m

Area of carpet = (22 - 2 × 0.75) (15.5 - 2 × 0.75)  = (22 - 1.5) (15.5 - 1.5)

Therefore,

area of the carpet = 20.5 × 14 = 287m²

portion uncovered = 341 - 287 = 54m²

a meter length of the carpet = 1 m × 0.82 m = 0.82m²

287/0.82 = 350m of carpet

cost of fencing the strip = Rs.60 per meter

cost of fencing the strip = 350 × 60  = Rs. 21000

Answer 2

Given :-

Length of the school hall = 22 m

Breadth of the school hall = 15.5

Margin of the carpet = 75 cm

Width of the carpet = 82 cm

To Find :-

The area of the carpet and the  area of the strip left uncovered.

The cost of fencing the strip.

Analysis :-

First find area of the hall and carpet using it's respective formula.

Subtract those two areas in order to get the portion uncovered.

Then find the cost by multiplying accordingly.

Solution :-

We know that,

• l = Length
• b = Breadth
• w = Width
• a = Area

By the formula,

$\underline{\boxed{\sf Area \ of \ rectangle=Length \times Breadth}}$

Given that,

Length of the school hall (l) = 22 m

Breadth of the school hall (b) = 15.5

Substituting their values,

Area of the hall = 22 × 15.5

Area = 341 m²

Given that, margin of the carpet = 75 cm

By converting,

100 cm = 1 m

Margin of carpet = 0.75 m

Next finding area of the carpet,

$\sf Area = (22 - 2 \times 0.75) (15.5 - 2 \times 0.75)$

$\sf = (22 - 1.5) (15.5 - 1.5)$

$\sf =20.5 \times 14$

$\sf =287 \ m^{2}$

Therefore, the area of the carpet is 287 m²

Portion uncovered = Area of the hall – Area of the carpet

Substituting their values,

Portion uncovered = 341 – 287

Portion uncovered = 54 m²

A meter length of the carpet = 1 × 0.82 = 0.82 m²

A meter length of the carpet = 287/0.82 = 350 m

Given that,

Cost of fencing the strip per meter = Rs. 60

Cost of fencing the strip = Meter length of the carpet × Cost per meter

Cost of fencing the strip = 350 × 60

= Rs. 21000

Therefore, the cost is Rs. 21000